The game is written as if everything was "done" ie: any stat requirement check is not cognizant of if that stat is actually unlockable to that point at time of release, merely that, eventually it will be. To do otherwise would significantly increase development complexity to no long-term benefit. Thresholds for physical skills will be in the 0.8.8 brains & brawn release, though note that you can also get cybernetics for +5 to str/stam/dex in released version.
This makes sense, although i'd argue in this particular situation the skill requirements are set too high -- one one hand, from "lore" viewpoint it seems reasonable, given it's company-wide competition. But on the other hand, from gameplay viewpoint, the player is likely to experience this event pretty early, even before the company retreat and the move to upper floors. At this stage having relevant skills even at 15 is a tall order, let alone 20. As such, having thresholds dropped from 20->15 and so on might be a sensible move.
And now, for something (almost) completely different -- speaking of things impossible, there's a much more serious issue i've run into. Since a picture is worth etc:
(the PC is a Senior Secretary)
In order to get promotion from Senior to Executive secretary the PC needs to work
140% of what is expected from them. However,
because of the 200% cap on their work, this is impossible, even if they work more hours than it's expected of them. 140% (promotion threshold from level 2->3) of expected 158% performance is 221% i.e. over 20% above the enforced 200% cap on all PC's efforts. With this cap in place, the best the PC can achieve is normally 126% of their expected 158% performance; in the pictured situation they managed to do slightly more thanks to nearly no work events (and it's still far cry from meeting the check)
This blocks a significant chunk of current content (relationship with PC's manager) and as such i don't believe is intended?
If it helps anything, the value of 158% comes from 100% x 1.2 (first promotion) x 1.2 (second promotion) x 1.1 (phase 4 chair intro) But even without chair multiplier it'd be 144% x 1.4 = 201.6% for the final promotion i.e. still above the efforts cap.